To do list of enhancing X-13ARIMA-SEATS

Halcyon: an enhancement of X-13ARIMA-SEATS 2022年9月12日

The following is a list of current enhancements to our in-house version of the X-13ARIMA-SEATS. Although from 1. to 4. are not directly related to holiday adjustments, they are necessary functions for our usage.

1. Memory management

The original X-13AS is very tight in memory.

Required memory to load the X-13AS which can adjust 1000 time series of 120 year monthly surged from X-12’s several Mega Bytes to nearly 2 Giga Bytes, which almost exceeds limit of MS-Windows Fortran application. Several arrays should be declared as dynamic arrays.

2. Trend-cycle factorisation of X-11 and composite series

Official versions of the X-13AS can detrend, i.e., factorise several TRAMO-SEATS series (original [a1], final adjusted [s11], and final trend-cycle [s12]) into long-term trend and cycle via Hodrick-Prescott filter. Change of several lines can adopt this option to final adjusted [d11], and final trend-cycle [d12] series of long time used X-11 series. Isn’t it interesting?

Original = Trend × Cycle × Irregular × Seasonal × Day of week × Holiday × Outliers and level shifts.

\(\mathtt{x11\lbrace } \)

\(\mathtt{\ \ \ hpcycle = [ yes | NO ] ( compute\ Hodrick\textrm{-}Prescott\ trend, default: no )}\)

\(\mathtt{\ \ \ hplan = ( smoothing\ parameter\ of\ the\ modi ed\ Hodrick\textrm{-}Prescott\ filter, default: computed )}\)

\(\mathtt{\ \ \ hprmls = [ yes | NO ] ( remove\ level\ shift\ from\ trend, default: no )}\)

\(\mathtt{\ \ \ hptarget = [ TREND | sadj | orig | sadjastc ] ( default: trend )}\)

\(\mathtt{\ \ \ \rbrace}\)

Argument hptarget selects the series to derive the long-term trend (T) and cycle (C).

\(\mathtt{Hptarget=trend}\): (T) derived from D12 (trend-cycle), (C) = D12/(T).

\(\mathtt{Hptarget=sadj}\): (T) derived from D11 (final adjusted), (C × I) = D11/(T).

\(\mathtt{Hptarget=orig}\): (T) derived from A1 (original), (C) = A1/(T).

\(\mathtt{Hptarget=sadjastc}\): (T) derived from D11, (C) = D11/(T).

3. Implanting Bry-Boschan turning point determination routine

Past average length of expansion and contraction, and length from the latest turning point are important benchmarks of forecast. I do not recommend to determine yourself visually, if your target consists from dozens of countries.

 Charlotte Boschan wrote near the beginning of “Cyclical Analysis of Time Series” that

“The determination of cyclical turning points, which is usually performed on seasonally adjusted time series, is an essential element of the National Bureau’s business cycle analysis”.

However, this routine should be implanted into certain seasonal adjustment program. Because if the seasonal adjustment program contains Bry-Boschan routine, you do not need to write a reading routine for the Bry-Boschan, and you do not need to write an output routine from X-13 to Bry-Boschan.

Ronny Nilsson and Gyorgy Gyomai wrote that the Phase Average Trend of the NBER, which contains Bry-Boschan routine, cannot treat series longer than 50 years. I completely agree with other discussions of this paper. But about this 50-year problem, my answer is that change parameter of your program from 50 to 150. My plan is to adjust thrice monthly (36 terms a year) series of 150 years for a while, and finally, daily series (average 365.2425 terms a year) of 150 yars.

4. Bundle

Note that almost all the economic time series have more than one series. Multiple series processing is the first capacity I added in the mid 1990’s based on the metafile run of the original X-12A.

5. Containing almost all the moving holidays of the world

I cannot imagine no one has been dreamed of the program like this.